Question

find g(x) for g(x) = x^(-1/9).
g(x) = \square

Explanation:

Step1: Apply power rule

The power rule states that if \(y = x^n\), then \(y^\prime=nx^{n - 1}\). For \(g(x)=x^{-\frac{1}{9}}\), where \(n =-\frac{1}{9}\).

Step2: Calculate derivative

\(g^\prime(x)=-\frac{1}{9}x^{-\frac{1}{9}-1}\)
Simplify the exponent: \(-\frac{1}{9}-1=-\frac{1 + 9}{9}=-\frac{10}{9}\)
So \(g^\prime(x)=-\frac{1}{9}x^{-\frac{10}{9}}\)

Answer:

\(g^\prime(x)=-\frac{1}{9}x^{-\frac{10}{9}}\)